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IEEE Computer Security Foundations Workshop (CSFW)

A Framework for the Sound Specification of Cryptographic Tasks

Juan A. Garay, Aggelos Kiayias, Hong-Sheng Zhou

Published Jul 1, 2010• 2 citations
Publisher

Abstract

Nowadays it is widely accepted to formulate the security of a protocol carrying out a given task via the “trustedparty paradigm,” where the protocol execution is compared with an ideal process where the outputs are computed by a trusted party that sees all the inputs. A protocol is said to securely carry out a given task if running the protocol with a realistic adversary amounts to “emulating” the ideal process with the appropriate trusted party. In the Universal Composability (UC) framework the program run by the trusted party is called an ideal functionality. While this simulation-based security formulation provides strong security guarantees, its usefulness is contingent on the properties and correct specification of the ideal functionality, which, as demonstrated in recent years by the coexistence of complex, multiple functionalities for the same task as well as by their “unstable” nature, does not seem to be an easy task. In this paper we address this problem, by introducing a general methodology for the sound specification of ideal functionalities. First, we introduce the class of canonical ideal functionalities for a cryptographic task, which unifies the syntactic specification of a large class of cryptographic tasks under the same basic template functionality. Furthermore, this representation enables the isolation of the individual properties of a cryptographic task as separate members of the corresponding class. By endowing the class of canonical functionalities with an algebraic structure we are able to combine basic functionalities to a single final canonical functionality for a given task. Effectively, this puts forth a bottom-up approach for the specification of ideal functionalities: first one defines a set of basic constituent functionalities for the task at hand, and then combines them into a single ideal functionality taking advantage of the algebraic structure. In our framework, the constituent functionalities of a task can be derived either directly or, following a translation strategy we introduce, from existing game-based definitions; such definitions have in many cases captured desired individual properties of cryptographic tasks, albeit in less adversarial settings. Our translation methodology entails a sequence of steps that systematically derive a corresponding canonical functionality given a game-based definition, effectively “lifting” the game-based definition to its composition-safe version. We showcase our methodology by applying it to a variety of basic cryptographic tasks, including commitments, digital signatures, zero-knowledge proofs, and oblivious transfer. While in some cases our derived canonical functionalities are equivalent to existing formulations, thus attesting to the validity of our approach, in others they differ, enabling us to “debug” previous definitions and pinpoint their shortcomings.

DOI
10.1109/csf.2010.26

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Nowadays it is widely accepted to formulate the security of a protocol carrying out a given task via the “trustedparty paradigm,” where the protocol execution is compared with an ideal process where the outputs are computed by a trusted party that sees all the inputs. A protocol is said to securely carry out a given task if running the protocol with a realistic adversary amounts to “emulating” the ideal process with the appropriate trusted party. In the Universal Composability (UC) framework the program run by the trusted party is called an ideal functionality. While this simulation-based security formulation provides strong security guarantees, its usefulness is contingent on the properties and correct specification of the ideal functionality, which, as demonstrated in recent years by the coexistence of complex, multiple functionalities for the same task as well as by their “unstable” nature, does not seem to be an easy task. In this paper we address this problem, by introducing a general methodology for the sound specification of ideal functionalities. First, we introduce the class of canonical ideal functionalities for a cryptographic task, which unifies the syntactic specification of a large class of cryptographic tasks under the same basic template functionality. Furthermore, this representation enables the isolation of the individual properties of a cryptographic task as separate members of the corresponding class. By endowing the class of canonical functionalities with an algebraic structure we are able to combine basic functionalities to a single final canonical functionality for a given task. Effectively, this puts forth a bottom-up approach for the specification of ideal functionalities: first one defines a set of basic constituent functionalities for the task at hand, and then combines them into a single ideal functionality taking advantage of the algebraic structure. In our framework, the constituent functionalities of a task can be derived either directly or, following a translation strategy we introduce, from existing game-based definitions; such definitions have in many cases captured desired individual properties of cryptographic tasks, albeit in less adversarial settings. Our translation methodology entails a sequence of steps that systematically derive a corresponding canonical functionality given a game-based definition, effectively “lifting” the game-based definition to its composition-safe version. We showcase our methodology by applying it to a variety of basic cryptographic tasks, including commitments, digital signatures, zero-knowledge proofs, and oblivious transfer. While in some cases our derived canonical functionalities are equivalent to existing formulations, thus attesting to the validity of our approach, in others they differ, enabling us to “debug” previous definitions and pinpoint their shortcomings.
Nowadays it is widely accepted to formulate the security of a protocol carrying out a given task via the "trusted-party paradigm," where the protocol execution is compared with an ideal process where the outputs are computed by a trusted party that sees all the inputs. A protocol is said to securely carry out a given task if running the protocol with a realistic adversary amounts to "emulating" the ideal process with the appropriate trusted party. In the Universal Composability (UC) framework the program run by the trusted party is called an ideal functionality. While this simulation-based security formulation provides strong security guarantees, its usefulness is contingent on the properties and correct specification of the ideal functionality, which, as demonstrated in recent years by the coexistence of complex, multiple functionalities for the same task as well as by their "unstable" nature, does not seem to be an easy task. In this paper we address this problem, by introducing a general methodology for the sound specification of ideal functionalities. First, we introduce the class of canonical ideal functionalities for a cryptographic task, which unifies the syntactic specification of a large class of cryptographic tasks under the same basic template functionality. Furthermore, this representation enables the isolation of the individual properties of a cryptographic task as separate members of the corresponding class. By endowing the class of canonical functionalities with an algebraic structure we are able to combine basic functionalities to a single final canonical functionality for a given task. Effectively, this puts forth a bottom-up approach for the specification of ideal functionalities: first one defines a set of basic constituent functionalities for the task at hand, and then combines them into a single ideal functionality taking advantage of the algebraic structure. In our framework, the constituent functionalities of a task can be derived either directly or, following a translation strategy we introduce, from existing game-based definitions; such definitions have in many cases captured desired individual properties of cryptographic tasks, albeit in less adversarial settings than universal composition. Our translation methodology entails a sequence of steps that derive a corresponding canonical functionality given a game-based definition. In this way, we obtain a well-defined mapping of game-based security properties to their corresponding UC counterparts. Finally, we demonstrate the power of our approach by applying our methodology to a variety of basic cryptographic tasks, including commitments, digital signatures, zero-knowledge proofs, and oblivious transfer. While in some cases our derived canonical functionalities are equivalent to existing formulations, thus attesting to the validity of our approach, in others they differ, enabling us to "debug" previous definitions and pinpoint their shortcomings.
What does it mean for a cryptographic protocol to be "secure"? Capturing the security requirements of cryptographic tasks in a meaningful way is a slippery business: On the one hand, we want security criteria that prevent "all potential attacks" against a protocol; on the other hand, we want our criteria not to be overly restrictive and accept "reasonable protocols". One of the main reasons for flaws is the often unexpected interactions among different protocol instances that run alongside each other in a composite system.This tutorial studies a general methodology for defining security of cryptographic protocols. The methodology, often dubbed the "trusted party paradigm", allows for defining the security requirements of a large variety of cryptographic tasks in a unified and natural way. We first review more basic formulations that capture security in isolation from other protocol instances. Next we address the security problems associated with protocol composition, and review formulations that guarantee security even in composite systems.
We propose a novel paradigm for defining security of cryptographic protocols, called universally composable security. The salient property of universally composable definitions of security is that they guarantee security even when a secure protocol is composed of an arbitrary set of protocols, or more generally when the protocol is used as a component of an arbitrary system. This is an essential property for maintaining security of cryptographic protocols in complex and unpredictable environments such as the Internet. In particular, universally composable definitions guarantee security even when an unbounded number of protocol instances are executed concurrently in an adversarially controlled manner, they guarantee non-malleability with respect to arbitrary protocols, and more. We show how to formulate universally composable definitions of security for practically any cryptographic task. Furthermore, we demonstrate that practically any such definition can be realized using known techniques, as long as only a minority of the participants are corrupted. We then proceed to formulate universally composable definitions of a wide array of cryptographic tasks, including authenticated and secure communication, key-exchange, public-key encryption, signature, commitment, oblivious transfer, zero knowledge and more. We also make initial steps towards studying the realizability of the proposed definitions in various settings.
Modeling security for protocols running in the complex network environment of the Internet can be a daunting task. Ideally, a security model for the Internet should provide the following guarantee: a protocol that implements a particular task specification will retain all the same security properties as the specification itself, even when an arbitrary set of protocols runs concurrently on the same network. This guarantee must hold even when other protocols are maliciously designed to interact badly with the analyzed protocol, and even when the analyzed protocol is composed with other protocols. The popular Universal Composability (UC) security framework aims to provide this guarantee. Unfortunately, such strong security guarantees come with a price: they are impossible to achieve without the use of some trusted setup. Typically, this trusted setup is global in nature, and takes the form of a Public Key Infrastructure (PKI) and/or a Common Reference String (CRS). However, the current approach to modeling security in the presence of such setups falls short of providing expected security guarantees. A quintessential example of this phenomenon is the deniability concern: there exist natural protocols that meet the strongest known security notions (including UC) while failing to provide the same deniability guarantees that their task specifications imply they should provide. We introduce the Generalized Universal Composability (GUC) framework to extend the UC security notion and enable the re-establishment of its original intuitive security guarantees even for protocols that use global trusted setups. In particular, GUC enables us to guarantee that secure protocols will provide the same level of deniability as the task specification they implement. To demonstrate the usefulness of the GUC framework, we first apply it to the analysis and construction of deniable authentication protocols. Building upon such deniable authentication protocols, we then prove a general feasibility result showing how to construct protocols satisfying our security notion for a large class of two-party and multi-party tasks (assuming the availability of some reasonable trusted setup). Finally, we highlight the practical applicability of GUC by constructing efficient protocols that securely instantiate two common cryptographic tasks: commitments and zero-knowledge proofs.
Universal composition framework, UC, provides a methodology for designing and analyzing protocols. A secure protocol/task can be formulated to an ideal functionality, translate some realistic schemes into an ideal protocol so that it can securely emulate the ideal functionality. UC theory ensures the security of protocols is maintained under a general protocol composition operation. Signature is a primary cryptographic task. The present formulation of ideal signature functionality is introduced and some flaws are pointed out, and then an improved signature functionality is presented and proven that it is securely realized by precisely those signature scheme that is equivalent to existential unforgery against chosen- message attacks, EU-CMA.
Universal composition framework, UC, provides a methodology for designing and analyzing protocols. A secure protocol/task can be formulated to an ideal functionality, translate some realistic schemes into an ideal protocol so that it can securely emulate the ideal functionality. UC theory ensures the security of protocols is maintained under a general protocol composition operation. Signature is a primary cryptographic task. The present formulation of ideal signature functionality is introduced and some flaws are pointed out, and then an improved signature functionality is presented and proven that it is securely realized by precisely those signature scheme that is equivalent to existential unforgery against chosen- message attacks, EU-CMA.